Abstract

A study of the magnetohydrodynamic system in which a nonmagnetized fluid
in a gravitational field is surrounded by a fluid carrying a vertical
magnetic field is presented. It is pointed out that this study can throw
some light on the fine-structural features of a sunspot. The equilibrium
configuration of the field-free fluid is a tapering column ending at an
apex. The regions away form the apex can be studied by the slender flux
tube approximation. A scheme developed to treat the apex indicates that,
just below the apex, the radius of the tapering column opens up with a
3/2 power dependence on the depth below the apex. If the internal
pressure of the field-free fluid is increased, the apex rises, and a
static equilibrium may not be possible beyond a limit if the magnetic
pressure drops quickly above a certain height. The nature of steady-flow
solutions beyond this limit is investigated. Under conditions inside a
sunspot, a column of field-free gas is found to rise with a velocity of
about 100 km/hr. If umbral dots and penumbral grains are interpreted as
regions where the field-free gas ultimately emerges, a very natural
explanation of most of their observed properties is obtained.

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